Twentieth-century chamber music

(2003). How Rare Is Symmetry in Musical 12-Tone Rows? The American Mathematical Monthly: Vol. 110, No. 2, pp. 124-132.

/pdf/how-rare-is-symmetry-in-musical-12-tone-rows-53sendzdaq.pdf

How rare is symmetry in musical 12-tone rows?

The relations of twelve-tone rows are of theoretical, analytical, and compositional interest. While relations based on the properties and transformations of rows have been widely studied, less attention has been paid to relations based on similarity. Formal similarity measures can be used to explicate ways of being similar. This study presents an analysis and categorization of 17 similarity measures for twelve-tone rows. Nine of them are new. The categorization of the similarity measures suggests the notion of different conceptions of twelve-tone rows. Five such conceptions are identified and explicated: vector, ordered pairs, subsegments, subsets, and interval contents. Similarity measures could thus be grouped into families based on the conception that they suggest. The similarity of twelve-tone rows allows two interpretations: comparison of the properties of the rows and the measurement of their transformational relations. The latter could be conveniently formalized using David Lewin’s Generalized Interval Systems as the framework. This allows the linking of the discussion on permutations in mathematics and computer science because the measurement of the complexity of a transformation coincides with the notion of presortedness of permutations. The study is in three parts. The first part gives an overview of the types of relations between twelve-tone rows, and presents a formalization of twelve-tone rows and row operations in terms of group theory. The second part focuses on the properties of similarity. By way of background a review and criticism of the literature on similarity in music theory is presented. The transformational approach and the metric are promoted. It is shown that transformational similarity measures create perfectly symmetrical spaces since every row is related to the other rows by precisely the same set of transformations. Since most of the similarity measures discussed in this study are dissimilarity measures of the distance between rows, the mathematical concept of the metric is applicable; many similarity measures define a metric. One of the main findings is that any metric for twelve-tone rows that is transformationally coherent under the operations generating row classes also defines a metric for those row classes. The third part discusses the similarity measures and the respective conceptions in detail. While the study focuses on the similarity of twelve-tone rows, the possibilities of extending the measures to the examination of other ordered pitch-class sets are also discussed. The work concludes with some examples of their analytical application.

On the similarity of twelve-tone rows

The songs of Mignon from Goethe's novel Wilhelm Meister's Apprenticeship (Wilhelm Meisters Lehrjahre) have been set hundreds of times by dozens of composers from the late 18th century onward. Though most frequently set by composers from the German School, Mignon's songs have also been popular with many non-Germans including works by French, Russian, and Italian composers. Mignon's mysterious persona has long fascinated song composers and many have been compelled to set her songs multiple times. The purpose of this study is to explore the character of Mignon from Goethe's novel, Wilhelm Meister's Apprenticeship through the lens of a psychoanalytic literary critic. I will examine six different composer's settings of Mignon's first song in the novel, "Kennst du das Land?" in order to understand how each composer portrays her character differently as seen through their unique compositional styles, their own psychology, and the style periods in which they wrote. The method of literary criticism applied to the song settings becomes psychoanalytic reader-response criticism as we move from merely analyzing Goethe's depiction of Mignon to each composer's depiction and reception of Goethe's character in addition to our own reception of that persona. One of the goals of this research is to show how Mignon's character is transformed as she makes her way through history in the development of Lieder.

/pdf/fragments-a-psychoanalytic-reading-of-the-character-mignon-qvd2qd34hn.pdf

Fragments: a psychoanalytic reading of the character Mignon on her journey through nineteenth century lieder

The importance of literature to Berg in the creation of his artistic world has generally been underestimated. Peter Altenberg was especially influential on the young Berg through their friendship, Berg9s reading of Altenberg9s works, and the relationship of Berg9s future wife with both men. Not only is a full understanding of the Altenberg Picture Postcard Texts crucial to the interpretation of Berg9s Altenberg Lieder, but Altenberg9s peculiar approaches to literary autobiography and vision of the role of women provided a model for Berg for this and subsequent works. Berg extracted five short texts from Altenberg9s full texts and rearranged them in a way that had special aesthetic and personal significance for himself. Important aspects of Berg9s musical setting relate directly to his treatment of the texts.

Alban Berg and Peter Altenberg: Intimate art and the aesthetics of life

The Music of Alban Berg

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The Music of Alban Berg